📚 Year 7 WJEC Statistics: Core Knowledge Review | Year 7 WJEC 统计：核心知识点梳理
Statistics is the branch of mathematics that deals with collecting, organising, presenting, analysing and interpreting data. In Year 7, you will build a solid foundation by learning about different types of data, how to gather information through surveys and experiments, and how to display that information using charts and graphs. You will also learn how to find simple averages and the range, as well as begin to understand the basics of probability. This article will guide you through the essential topics for the WJEC Year 7 Statistics curriculum, helping you to review key ideas and check your understanding.
统计学是数学的一个分支，研究数据的收集、整理、展示、分析和解读。在七年级，你将打下坚实的基础，学习不同的数据类型、如何通过调查和实验收集信息，以及如何使用图表展示信息。你还会学习如何计算简单的平均数和极差，并开始理解概率的基础知识。本文将带你梳理 WJEC 七年级统计课程的核心主题，帮助你复习关键概念并检测自己的理解程度。
1. What is Statistics? | 什么是统计学？
Statistics is the science of data. Whenever we ask a question like “What is the most popular crisp flavour in our class?” or “How tall are Year 7 students?”, we are dealing with statistics. The subject involves planning how to collect data, gathering it fairly, organising it into tables, drawing graphs, and then interpreting what the graphs and numbers tell us. In Year 7, you will learn the first steps of this process: from posing a question to drawing simple conclusions.
统计学是关于数据的科学。每当我们提出“班上最受欢迎的薯片口味是什么？”或“七年级学生有多高？”这样的问题时，我们就在处理统计问题。这门学科包括规划如何收集数据、公平地采集数据、将数据整理成表格、绘制图表，然后解读图表和数字所传达的信息。在七年级，你将学习这个过程的第一步：从提出一个问题到得出简单的结论。
Good statistical thinking helps us make sense of the world. For example, a shop owner might use statistics to decide which products to stock, and a sports coach might use statistics to improve a team’s performance. All of this begins with understanding basic statistical vocabulary and techniques.
良好的统计思维帮助我们理解世界。例如，店主可能会利用统计学决定进货哪些产品，体育教练可能会利用统计学提高队伍的表现。这一切都始于掌握基本的统计词汇和方法。
2. Types of Data | 数据类型
Data can be split into two main types: categorical data and numerical data. Categorical data (also called qualitative data) describes qualities or categories that cannot be measured with numbers, but can be counted. Examples include favourite colour, pet type, or eye colour. Numerical data (also called quantitative data) involves numbers that can be measured or counted. Examples include height, number of siblings, or test scores.
数据可以分为两大类：分类数据和数值数据。分类数据（也称定性数据）描述无法用数字测量但可以计数的品质或类别，例如最喜欢的颜色、宠物种类或眼睛颜色。数值数据（也称定量数据）涉及可以测量或计数的数字，例如身高、兄弟姐妹的数量或考试成绩。
Numerical data can be further divided into discrete and continuous data. Discrete data can only take certain values, usually whole numbers, like the number of cars in a car park (you can’t have 2.5 cars). Continuous data can take any value within a range, like height (you might be 134.7 cm). Understanding data types helps you choose the best way to display your information later.
数值数据还可以细分为离散数据和连续数据。离散数据只能取某些特定的值，通常是整数，比如停车场里的汽车数量（你不能有2.5辆车）。连续数据可以取一个范围内的任何值，比如身高（你可能是134.7厘米）。理解数据类型有助于你之后选择最佳的展示方式。
3. Collecting Data | 数据收集
Before you can work with data, you need to collect it. Data can be collected through surveys (questionnaires), observations, or experiments. In Year 7, you will often design simple questionnaires. A good question must be clear and unbiased. For example, instead of asking “Do you agree that football is the best sport?”, which pushes people towards an answer, you should ask “What is your favourite sport?” and provide a few options.
在使用数据之前，你需要先收集数据。数据可以通过调查（问卷）、观察或实验来收集。在七年级，你经常会设计简单的问卷。好的问题必须清晰、不带偏见。例如，与其问“你是否同意足球是最好的运动？”——这会把人们推向某个答案，不如问“你最喜欢的运动是什么？”并提供几个选项。
When collecting data, it is also important to think about the sample. For a survey about school lunches, you might ask everyone in your class (a census) or just a selection of students (a sample). The sample should represent the whole group fairly to avoid biased results. You will also learn to use tally charts to record data quickly and accurately.
收集数据时，还需要考虑样本。对于关于学校午餐的调查，你可以询问全班每个人（普查），或者只询问一部分学生（抽样）。样本应该公平地代表整个群体，以避免结果有偏。你还将学习使用计数符号快速准确地记录数据。
4. Frequency Tables | 频数表
A frequency table is a way of organising raw data so that it is easier to understand. In the table, you list each category or value and then count how many times it appears (the frequency). Often, a tally column is used to help with counting. For example, if you asked 20 students their favourite fruit and got responses like ‘apple, banana, apple, orange, banana, apple…’, you could record this in a frequency table.
频数表是一种整理原始数据的方法，使数据更容易理解。在表格中，你列出每个类别或数值，然后统计它出现的次数（即频数）。通常会用一个计数列来帮助统计。例如，如果你询问了20名学生最喜欢的水果，得到“苹果、香蕉、苹果、橙子、香蕉、苹果……”这样的回答，就可以用频数表记录下来。
| Fruit | Tally | Frequency |
|---|---|---|
| Apple | IIII | 4 |
| Banana | IIIII I | 6 |
| Orange | IIIII | 5 |
| Grapes | IIIII | 5 |
From the frequency table, you can quickly see that banana is the most popular fruit and apple is the least popular among these four. Frequency tables are the starting point for many statistical diagrams.
从频数表中，你可以快速看出香蕉是最受欢迎的水果，苹果在这四种中最不受欢迎。频数表是许多统计图表的起点。
5. Bar Charts and Pictograms | 条形图和象形图
Bar charts are used to display categorical data or discrete numerical data. Each category is shown as a bar, and the height of the bar represents the frequency. It is important that the bars have equal width and that there are gaps between them (for categorical data). You must label the axes and give the chart a title. Bar charts make it easy to compare categories at a glance.
条形图用于展示分类数据或离散数值数据。每个类别用一根条形表示，条形的高度代表频数。重要的是，所有条形的宽度要相等，且条形之间要有间隔（对于分类数据）。你必须标注坐标轴并为图表加上标题。条形图让人一眼就能比较各个类别。
A pictogram uses simple pictures or symbols to represent data. Each picture stands for a certain number of items. For instance, in a pictogram showing the number of books read by students, one book icon might represent 2 books. A half icon would then represent 1 book. Pictograms are visually appealing but require a key to explain what each symbol means.
象形图使用简单的图画或符号来表示数据。每个图画代表一定数量的项目。例如，在一幅展示学生读书数量的象形图中，一本书的图标可能代表2本书，半个图标则代表1本书。象形图在视觉上很有吸引力，但需要一个图例来解释每个符号的含义。
6. Pie Charts | 饼图
A pie chart is a circular chart divided into sectors, each showing the proportion of a category relative to the whole. The entire circle represents the total frequency. Pie charts are excellent for showing how a whole is split into parts. To interpret a pie chart, you compare the sizes of the angles or areas. The larger the sector, the bigger the proportion.
饼图是一种分成若干扇区的圆形图表，每个扇区显示某个类别相对于整体的比例。整个圆代表总频数。饼图非常适合展示整体如何分成各个部分。解读饼图时，你要比较扇区角度或面积的大小。扇区越大，所占比例就越大。
In Year 7, you may construct simple pie charts using fractions. For example, if 1/4 of the students chose ‘walking’ as their way to school, the ‘walking’ sector would be 1/4 of the circle, or 90°. You will learn that the angle of a sector can be calculated as (category frequency ÷ total frequency) × 360°.
在七年级，你可能会用分数来构造简单的饼图。例如，如果有1/4的学生选择“步行”上学，那么“步行”的扇区就是圆的1/4，即90°。你将学会计算扇区角度的方法：（类别频数÷总频数）×360°。
7. Line Graphs | 线图
Line graphs are used to show how numerical data changes over time or another continuous variable. Points are plotted on a coordinate grid and joined with straight lines. The horizontal axis usually represents time (days, months, years), and the vertical axis shows the quantity you are measuring. Line graphs help us spot trends, such as an increase in temperature throughout the day.
线图用于展示数值数据如何随时间或其他连续变量变化。它在坐标格上标出数据点，然后用直线连接。横轴通常代表时间（天、月、年），纵轴显示你测量的量。线图能帮助我们识别趋势，比如一天中气温的升高。
When reading a line graph, ask yourself: What is the overall pattern? Is it going up, down, or staying level? Are there any sudden changes? You should also be careful with the scales – a broken scale can make changes look bigger or smaller than they really are. Always check the numbers before drawing conclusions.
阅读线图时，要问自己：整体模式是什么？是上升、下降还是持平？有没有突然的变化？你还要注意刻度——断裂的刻度可能会让变化看起来比实际更大或更小。在得出结论之前，一定要检查数字。
8. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph (or scatter plot) is used to show the relationship between two sets of numerical data. Each point on the graph represents one item with two measurements. For instance, you might plot the height and arm span of several students. The pattern of the points can suggest whether there is a correlation between the two variables.
散点图用来展示两组数值数据之间的关系。图上的每个点代表一条有两个测量值的记录。例如，你可以标出几名学生的身高和臂展。点的分布模式可以表明两个变量之间是否存在相关性。
Correlation describes the strength and direction of a relationship. Positive correlation means as one variable increases, the other also tends to increase (e.g. more revision and higher test marks). Negative correlation means as one variable increases, the other tends to decrease (e.g. more hours of TV and lower test marks). No correlation means there is no clear pattern. In Year 7, you will mainly interpret scatter graphs rather than draw detailed lines of best fit.
相关性描述关系的强度和方向。正相关意味着当一个变量增加时，另一个也倾向于增加（例如，复习时间越多，考试成绩越高）。负相关意味着当一个变量增加时，另一个倾向于减少（例如，看电视的时间越多，考试成绩越低）。无相关意味着没有清晰的模式。在七年级，你主要是解读散点图，而不必绘制详细的最佳拟合线。
9. Averages: Mode, Median and Mean | 平均数：众数、中位数和均值
An average is a single value that summarises a set of data, showing what a ‘typical’ value is. There are three main averages you need to know: the mode, the median, and the mean. Each one is useful in different situations.
平均数是概括一组数据的单个数值，显示“典型”的值是什么。你需要了解三种主要的平均数：众数、中位数和均值。它们在不同情形下各有用处。
The mode is the value that appears most often. To find the mode, you just look for the highest frequency. A set can have one mode, more than one mode (bimodal), or no mode at all if all values are different. The median is the middle value when the data is arranged in order. If there are two middle numbers, the median is halfway between them. The mean is what many people call the ‘average’. It is calculated by adding up all the values and then dividing by how many values there are.
众数是出现次数最多的值。找众数时，只需看哪个值的频数最高。一组数据可以有一个众数、多个众数（双众数），或者如果所有值都不相同则没有众数。中位数是将数据按顺序排列后位于中间的值。如果有两个中间数，中位数就是这两个数的平均数。均值就是许多人所说的“平均数”，计算方法是把所有数值加起来，再除以数值的个数。
Mean = (Sum of all values) ÷ (Number of values)
均值 = 所有数值的总和 ÷ 数据的个数
Example: For the data set 3, 5, 7, 7, 10, the mode is 7 (appears twice), the median is 7 (middle score), and the mean is (3+5+7+7+10) ÷ 5 = 32 ÷ 5 = 6.4. The range would be 10 − 3 = 7.
举例：对于数据集3, 5, 7, 7, 10，众数是7（出现两次），中位数是7（中间数值），均值是（3+5+7+7+10）÷5 = 32÷5 = 6.4。极差是10−3=7。
10. Range | 极差
The range is a measure of spread. It tells you how spread out the data values are. The range is simply the difference between the largest and the smallest values in the data set.
极差是衡量数据分散程度的指标。它告诉你数据值的分布有多广。极差仅仅是数据集中最大值与最小值之间的差值。
Range = Largest value − Smallest value
极差 = 最大值 − 最小值
A small range means the data values are quite close together; a large range means they are more spread out. For example, if two classes sat the same test and Class A had scores from 45 to 55 (range = 10) while Class B had scores from 20 to 90 (range = 70), we can say that Class A’s scores are more consistent. The range is easy to calculate but is affected by extreme values (outliers).
极差小意味着数据值比较集中；极差大意味着数据值分布更广。例如，如果两个班参加同样的考试，A班的分数从45到55（极差为10），而B班的分数从20到90（极差为70），我们可以说A班的分数更稳定。极差计算简单，但容易受极端值（离群值）的影响。
11. Introduction to Probability | 概率入门
Probability is the branch of mathematics that studies how likely events are to happen. Probability is measured on a scale from 0 to 1. A probability of 0 means an event is impossible (e.g., rolling a 7 on a normal six-sided die). A probability of 1 means an event is certain (e.g., the sun will rise tomorrow). The probability of an event that is equally likely to happen or not happen is 1/2, like getting a head when flipping a fair coin.
概率是研究事件发生可能性的数学分支。概率的度量范围是从0到1。概率为0表示事件不可能发生（例如，在普通的六面骰子上掷出7点）。概率为1表示事件必然发生（例如，明天太阳会升起）。发生与不发生的可能性相等的事件的概率是1/2，比如抛一枚公平硬币得到正面。
To find the probability of an event, you can use the formula:
要求一个事件的概率，可使用以下公式：
Probability = (Number of favourable outcomes) ÷ (Total number of possible outcomes)
概率 = 有利结果的数量 ÷ 所有可能结果的总数
For a six-sided die, the probability of rolling an even number is 3/6 = 1/2, because there are 3 even outcomes (2, 4, 6) out of 6 possible outcomes. You can also write probabilities as fractions, decimals or percentages, but in Year 7 you will most often use fractions in their simplest form and words like ‘unlikely’, ‘even chance’ and ‘likely’.
对于六面骰子，掷出偶数的概率是3/6=1/2，因为6个可能结果中有3个偶数结果（2、4、6）。你也可以用小数或百分数表示概率，但在七年级，你通常使用最简分数以及“不太可能”“机会均等”“很可能”等词语。
Understanding probability helps you make predictions and describe the level of risk in everyday situations, from weather forecasts to games.
理解概率有助于你做出预测，并描述从天气预报到游戏中日常情境的风险水平。
Published by TutorHao | Statistics Revision Series | aleveler.com
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